Problem: Solve for $x$ and $y$ using substitution. ${x-3y = -7}$ ${x = -6y+11}$
Answer: Since $x$ has already been solved for, substitute $-6y+11$ for $x$ in the first equation. ${(-6y+11)}{- 3y = -7}$ Simplify and solve for $y$ $-6y+11 - 3y = -7$ $-9y+11 = -7$ $-9y+11{-11} = -7{-11}$ $-9y = -18$ $\dfrac{-9y}{{-9}} = \dfrac{-18}{{-9}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x = -6y+11}\thinspace$ to find $x$ ${x = -6}{(2)}{ + 11}$ $x = -12 + 11$ ${x = -1}$ You can also plug ${y = 2}$ into $\thinspace {x-3y = -7}\thinspace$ and get the same answer for $x$ : ${x - 3}{(2)}{= -7}$ ${x = -1}$